Non-Markovian theory of activated rate processes. VI. Unimolecular reactions in condensed phases

Abstract

The non-Markovian theory of activated rate processes developed by Carmeli and Nitzan is applied to investigate unimolecular reactions in condensed phases with particular emphasis on the molecular size (number of internal degrees of freedom) dependence of the effect of solvent friction on the reaction rate. The model consists of one reaction coordinate coupled to n−1 nonreactive modes. The molecule solvent interaction is treated within the context of the generalized Langevin equation. The reaction dynamics may be roughly described as two consecutive processes: the well (energy diffusion) dynamics where it is assumed that fast intramolecular vibrational relaxation and slower overall molecular energy diffusion dominate the process, and the barrier dynamics where it is assumed that the motion along the reaction coordinate is only weakly coupled to the nonreactive modes. This model leads to a result for the reaction rate which, as in the one-dimensional case, is obtained as the inverse of the sum of two times: the barrier crossing time and the energy diffusion time. The latter is very sensitive to molecular size and becomes extremely short for large molecules. Correspondingly, the Kramers turnover region is predicted to occur for low molecular weight solvent in the high pressure gas phase, as was found in recent experiments. For higher viscosities the rate is dominated by the barrier crossing time with a large (larger for larger molecules) transition state rate plateau and with a falloff for high viscosities. Recent interesting results by Straub et al. which have pointed out the dominance of spatial diffusion in the well for extremely high viscosities (overdamped well motion) are argued to be irrelevant for most molecular situations.